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- Basic Math and Science Data Interpretation and Probability Questions and Answers Flashcards

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  1. A dataset of 9 values has a mean of 14. When the largest value is removed, the remaining 8 values have a mean of 12. What was the largest value in the original dataset?

    Answer: 30

    The original sum of all 9 values is 9 × 14 = 126. After removing the largest value, the sum of the remaining 8 values is 8 × 12 = 96. The largest value equals 126 − 96 = 30.

  2. A bag contains 5 red, 3 blue, and 2 green marbles. Two marbles are drawn without replacement. What is the probability that both marbles are the same color?

    Answer: 14/45

    P(both red) = (5/10)(4/9) = 20/90. P(both blue) = (3/10)(2/9) = 6/90. P(both green) = (2/10)(1/9) = 2/90. Total = 28/90 = 14/45.

  3. A scatter plot of 6 students' study hours (x) vs. test scores (y) yields a line of best fit passing through (1, 54) and (6, 79). What is the residual for the student who studied 4 hours and scored 70?

    Answer: +1 (scored above the predicted value)

    Slope = (79 − 54) / (6 − 1) = 25/5 = 5. Using point-slope form: y = 54 + 5(x − 1) = 5x + 49. At x = 4: predicted score = 5(4) + 49 = 69. Residual = actual − predicted = 70 − 69 = +1.

  4. In a survey of 200 adults, 120 drink coffee, 80 drink tea, and 40 drink both. If a participant is selected at random from those who drink at least one of the two beverages, what is the probability the selected person drinks coffee but NOT tea?

    Answer: 1/2

    Coffee-only drinkers = 120 − 40 = 80. Tea-only = 80 − 40 = 40. Both = 40. At least one beverage = 80 + 40 + 40 = 160 people. P(coffee only | at least one) = 80/160 = 1/2.

  5. A scientist records river pH values over 7 days: 6.8, 7.1, 7.4, 6.9, 7.6, 6.7, 7.5. What is the interquartile range (IQR)?

    Answer: 0.7

    Sorted: 6.7, 6.8, 6.9, 7.1, 7.4, 7.5, 7.6. Median (Q2) = 7.1. Lower half {6.7, 6.8, 6.9}: Q1 = 6.8. Upper half {7.4, 7.5, 7.6}: Q3 = 7.5. IQR = 7.5 − 6.8 = 0.7.

  6. A quality-control chart shows Factory A produces 250 units/day with a 4% defect rate, and Factory B produces 750 units/day with a 2% defect rate. If one unit is chosen at random from the combined daily output, what is the probability it is defective?

    Answer: 2.5%

    Factory A defects: 250 × 0.04 = 10. Factory B defects: 750 × 0.02 = 15. Total units: 1000. Total defects: 25. P(defective) = 25/1000 = 2.5%.